Truth Through Proof defends an anti-platonist philosophy of
mathematics derived from game formalism. Classic formalists claimed
implausibly that mathematical utterances are truth-valueless moves
in a game. Alan Weir aims to develop a more satisfactory successor
to game formalism utilising a widely accepted, broadly neo-Fregean
framework, in which the proposition expressed by an utterance is a
function of both sense and background circumstance. This framework
allows for sentences whose truth-conditions are not
representational, which are made true or false by conditions
residing in the circumstances of utterances but not transparently
in the sense.
Applications to projectivism and fiction pave the way for the claim
that mathematical utterances are made true or false by the
existence of concrete proofs or refutations, though these
truth-making conditions form no part of their sense or
informational content.
The position is compared with rivals, an account of the
applicability of mathematics developed, and a new account of the
nature of idealisation proffered in which it is argued that the
finitistic limitations Godel placed on proofs are without rational
justification. Finally a non-classical logical system is provided
in which excluded middle fails, yet enough logical power remains to
recapture the results of standard mathematics.
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